Hmm, very good. The language is very descriptive and paints a clear picture of the story, and the characterization is good, although at times the protagonist, Lucifer, seems a bit too perfect. I particularly like the way Lucifer doesn't know what is happening around him, which is good compared to many stories I've read or even written myself where the protagonist knows exactly what to do, or has a close friend fit that role. The way the thoughts and feelings of Lucifer cut clearly to you marks a good writing quality. I've noticed that many good stories put you in the protagonist's position, and that's exactly what's happening here.
However, this fanfic has its flaws. I already mentioned that Lucifer sometimes seems too perfect, and other characters seem to be in the story for little reason at all. Giving these characters other roles would help, and you could fix Lucifer's problem by adding a couple of character flaws that challenge him. Not knowing anything is a start, but by itself doesn't work. Maybe he approaches this issue less than perfectly, showing a character flaw that may recur through the story.
Then there's the problem that none of the many questions in the story have answers. This leaves me somewhat confused, depending on the action to understand everything. While the confusion may be the technique that marks this story apart from the others, it would be nice if some questions were answered at some point in the story.
Finally, there seems to be a chapter sequence involving a fight scene, a conversation, and some other challenge against Lucifer (for example, Sophia's house catching on fire, Xandra switching sides, conflicts with Wade, etc.). Each chapter somehow seems to repeat the earlier ones. A good way to fix this would be to have chapters focus on one or two connected events, like an entire chapter that's a fight scene, or for the "house on fire" incident, you could end the previous chapter with Lucifer discovering the burning house, and then have the next chapter end with Sophia blacking out just before revealing what was stolen.
Perhaps what I'm driving at is that the chapters are too broad, and end weakly. One technique I've picked up is to leave a chapter with some problem. I gave an example in the last paragraph, but there are many other ways. You could have had Lucifer smell something burning first, then in the next chapter actually find the burning house and end with the Croagunk's ambush.
All in all though, this is very good, and I say this because I've written fanfics myself, and this goes beyond them. Keep it up, Aura.